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http://dx.doi.org/10.22771/nfaa.2022.27.02.14

DECOMPOSITION FOR CARTAN'S SECOND CURVATURE TENSOR OF DIFFERENT ORDER IN FINSLER SPACES  

Abdallah, Alaa A. (Department of Mathematics, Faculty of Education, Abyan University, Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University)
Navlekar, A.A. (Department of Mathematics, Pratishthan Mahavidyalaya, Science College Dr. Babasaheb Ambedkar Marathwada University)
Ghadle, Kirtiwant P. (Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University)
Hamoud, Ahmed A. (Department of Mathematics, Taiz University)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.2, 2022 , pp. 433-448 More about this Journal
Abstract
The Cartan's second curvature tensor Pijkh is a positively homogeneous of degree-1 in yi, where yi represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pijkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.
Keywords
Decomposition of Cartan's second curvature tensor $P^{i}_{jkh}$; Berwald covariant derivative; generalized BP-recurrent space; generalized BP-birecurrent space;
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Times Cited By KSCI : 1  (Citation Analysis)
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